Ionizing particles (alpha & beta)

I think I understand the impact that an alpha particle can have on living tissue.
Not having electrons in it valence it would be very reactive - stripping electrons from atoms or molecules it bumps into (assuming it made its way in a biotic host).

But how does a beta particle ionize an atom or molecule? If the target atom/molecule had a full valence wouldn't the beta particle just get deflected? And, if it were to join a full valence wouldn't it just knock another electron out, leaving the initial target atom/molecule unchanged?

Regarding gamma rays, how exactly do they interact with an atom/molecule? How does a photon ionize an atom/molecule?

I don't really know, but I would guess that a [tex]\beta^-[/tex] particle (which is just an electron) can come with a lot of kinetic energy, so it would probably collide with another electron and transfer enough energy to that electron to escape the atom/molecule that it is bound to. If it doesn't have enough energy for that it would probably be absorbed by some molecule that is moderately stable, ionizing it. [tex]\beta^+[/tex] particles are positrons, and annihiliate with electrons releasing at least 2mc^2 = 1.022 MeV in energy in, probably gamma rays (which may go on to ionizing other stuff, as well as already having ionized something by annihilating an electron).

Gamma rays are very high energy (> 100 keV), if a gamma ray was absorbed by an electron it would certainly have enough energy to escape whatever bound state it was in, and would probably end up colliding with several other electrons and ionizing nearby molecules before it runs out of energy.

Energy and momentum (4-momenta) is transferred between charged particles due to the Coulomb interaction, which has infinite range. So we should not think of this as biliard balls colliding, but instead an incoming wave function interacting with the coulomb potentials that is generated by the atomic electrons and the atomic nucleus.

And if you know you scattering theory, you can calculate the probability for transfering an amount of energy that can excite and ionize and atom. And then calculate the accumulated effect, this is done in the Bethe-Bloch formula.

For charged particles also undergo radiative losses, due to the change in momentum vector (i.e acceleration), and this process leads to bremsstrahlung, since accelerated charge emits EM-waves (i.e. photons). This process is dominating over the ionization energy losses when we have light particles, i.e electrons.

Photons interact with matter with 3 processes; pair-production - compton scattering & Photoelectric effect. In the latter, the photon can be absorbed by the atomic electron and if the energy of the photon is higher than then ionization energy, the electron will leave the atom - i.e the atom becomes ionized.